Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#2010 |
| Fitting | C3×#2010 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2010 |
2190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | #72214634, D3×#23882, D3×#23897, … |
| maximal normal subgroup of | D3×#23882, D3×#23897, C2×D3×#2010, … |
| maximal quotient of | #72214634, C2×D3×#2010, #72248356, … |
| automorphism group of | #4466 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196582);